Volume Calculator
How it Works
01Select Shape
Choose from 7 geometric solids
02Choose Units
Toggle between Metric (cm, m) and Imperial (in, ft) units
03Enter Data
Input the required dimensions like radius, height, or side lengths
04Compute Yield
Process the geometry to receive an instant volumetric result
What is a Volume Calculator?
Volume is the measure of three-dimensional space enclosed by a boundary. It answers a fundamental question in physics, engineering, and everyday life: "How much space does this object occupy?" Whether you're an architect sizing a concrete pour, a student solving solid geometry, or a shipping manager calculating dimensional weight, precise volume computation is non-negotiable.
Our Volume Calculator supports 14 geometric shapes — from basic cubes and spheres to advanced forms like conical frustums, ellipsoids, and hollow cylinders. Each calculation uses high-precision floating-point arithmetic with π computed to 15 decimal places, ensuring accuracy suitable for professional engineering and scientific applications.
The integrated multi-unit engine allows you to input each dimension in a different unit (e.g., radius in centimeters, height in feet) and receive results in your chosen output unit. All conversions happen internally using a unified metric base (cm), eliminating manual conversion errors entirely.
Pro Tip: For more relevant tools in the math and science category, try our Calculate Percentage.
How do I calculate the volume of a shape?
Every 3D shape has a unique volume formula. Here is the complete reference for all 14 shapes supported by our calculator:
All formulas use standard mathematical notation. π ≈ 3.14159265358979 is used for shapes with circular cross-sections.
Basic Solids — Prisms & Cubes:
V = s³
Where s is the side length. All edges are equal.
Example: A cube with s = 5 cm → V = 5³ = 125 cm³
V = l × w × h
Where l = length, w = width, h = height.
Example: A box 10×5×2 m → V = 100 m³ (100,000 liters)
V = (½ × b × ht) × L
Where b = triangle base, ht = triangle height, L = prism length.
Example: b=6, ht=4, L=10 → V = (½×6×4)×10 = 120 cm³
V = (1/3) × b² × h
Where b = base edge, h = perpendicular height.
Example: b=10, h=15 → V = (1/3)×100×15 = 500 cm³
Circular Solids — Cylinders, Cones & Spheres:
V = πr²h
Where r = radius, h = height.
Example: r=7, h=10 → V = π×49×10 = 1,539.38 cm³
V = (1/3)πr²h
Exactly one-third the volume of a cylinder with the same base and height.
Example: r=5, h=12 → V = (1/3)×π×25×12 = 314.16 cm³
V = (4/3)πr³
Where r = radius. A sphere encloses the maximum volume for a given surface area.
Example: r=10 → V = (4/3)×π×1000 = 4,188.79 cm³
V = (2/3)πr³
Exactly half the volume of a sphere. Common in dome and bowl calculations.
Example: r=10 → V = (2/3)×π×1000 = 2,094.40 cm³
Advanced Solids — Frustums, Capsules & Ellipsoids:
V = (πh/3)(R² + Rr + r²)
A cone with the top sliced off. R = bottom radius, r = top radius.
Example: R=8, r=4, h=6 → V = (π×6/3)(64+32+16) = 703.72 cm³
V = (h/3)(A₁ + A₂ + √(A₁A₂))
Where A₁ = bottom base area, A₂ = top base area.
Example: b1=10, b2=6, h=8 → V = (8/3)(100+36+60) = 522.67 cm³
V = (4/3)π × a × b × c
A "stretched sphere" with three semi-axes: a, b, and c.
Example: a=5, b=3, c=4 → V = (4/3)×π×60 = 251.33 cm³
V = πr²L + (4/3)πr³
A cylinder capped by two hemispheres. r = radius, L = cylinder length.
Example: r=3, L=10 → V = π×9×10 + (4/3)×π×27 = 396.00 cm³
V = πh(R² − r²)
Where R = outer radius, r = inner radius, h = height.
Example: R=10, r=8, h=20 → V = π×20×(100-64) = 2,261.95 cm³
V = (πh²/3)(3R − h)
A "dome" sliced from a sphere. R = sphere radius, h = cap height.
Example: R=10, h=3 → V = (π×9/3)(30-3) = 254.47 cm³
Volume Calculator – 3D Geometric Volume & Capacity Tool In Practice
- Step 1: Select "Rectangular Prism (box)" from the shape dropdown.
- Step 2: Enter Length = 10, Width = 5, Height = 2, all in meters.
- Step 3: Set output unit to m³.
- Step 4: Result: 100.00 m³ — equivalent to 100,000 liters or 26,417 US gallons.
- This tells you the pool needs 100 cubic meters of water to fill completely.
Mixed-Unit Example: Calculate a cylindrical tank with radius in inches (r = 18 in) and height in feet (h = 4 ft). Our engine converts both to centimeters internally, computes πr²h, and returns the result in your chosen output unit — no manual conversion needed.
Volume benchmarks (Scale Reference)
Volume Unit Conversion Reference
Volume can be expressed in many units depending on the context — cubic meters for construction, liters for liquid capacity, or cubic inches for machining. Here is the complete conversion reference:
| From | To | Multiply By |
|---|---|---|
| 1 m³ | Liters | 1,000 |
| 1 m³ | US Gallons | 264.172 |
| 1 m³ | Cubic Feet | 35.3147 |
| 1 m³ | Cubic Inches | 61,023.7 |
| 1 ft³ | Liters | 28.3168 |
| 1 ft³ | US Gallons | 7.48052 |
| 1 Liter | cm³ (mL) | 1,000 |
| 1 US Gallon | Liters | 3.78541 |
Pro Tip: 1 mL = 1 cm³ exactly. This means a 500 mL water bottle has an internal volume of exactly 500 cubic centimeters.
Volume in Real-World Engineering
Volume calculations underpin critical decisions across every engineering discipline. Here are the most common real-world applications where precise volumetric analysis matters:
🏗️ Concrete & Construction
Estimating concrete for slabs (cuboid), columns (cylinder), and footings (frustum). A 10×10×0.15m slab needs exactly 15 m³ of concrete — about 2.5 truckloads.
🚢 Shipping & Logistics
Carriers charge by "dimensional weight" (L×W×H ÷ 5000). A 60×40×40 cm box has a DIM weight of 19.2 kg — even if the actual product weighs only 5 kg.
⚗️ Chemistry & Pharmaceuticals
Capsule volume (cylinder + two hemispheres) determines drug dosage. A standard Size 0 capsule holds approximately 0.68 mL (cm³) of powder.
🏠 Home & Garden
Pool water volume, aquarium capacity, raised garden bed soil (cuboid), and round planter pots (cylinder). A 4-foot diameter, 2-foot deep kiddie pool holds about 188 liters.
🛢️ Industrial Storage
Cylindrical tank capacity for oil, water, and chemicals. Spherical tanks (like LNG storage) maximize volume-to-surface-area ratio, minimizing heat loss.
📐 3D Printing & CAD
Estimating filament usage and print cost. Volume directly determines material consumption — a solid 5 cm cube uses 125 cm³ of filament (about 150g of PLA).
Who Should Use the Volume Calculator?
Technical Reference
Key Takeaways
Frequently Asked Questions
What is the ?
Volume is the measure of three-dimensional space enclosed by a boundary. It answers a fundamental question in physics, engineering, and everyday life: "How much space does this object occupy?" Whether you're an architect sizing a concrete pour, a student solving solid geometry, or a shipping manager calculating dimensional weight, precise volume computation is non-negotiable.
Our Volume Calculator supports 14 geometric shapes — from basic cubes and spheres to advanced forms like conical frustums, ellipsoids, and hollow cylinders. Each calculation uses high-precision floating-point arithmetic with π computed to 15 decimal places, ensuring accuracy suitable for professional engineering and scientific applications.
The integrated multi-unit engine allows you to input each dimension in a different unit (e.g., radius in centimeters, height in feet) and receive results in your chosen output unit. All conversions happen internally using a unified metric base (cm), eliminating manual conversion errors entirely.
Pro Tip: For more relevant tools in the math and science category, try our Calculate Percentage.
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Author Spotlight
The ToolsACE Team
Our math tools team implements volume formulas for 10+ 3D shapes — sphere (V=4/3πr³), cylinder (V=πr²h), cone (V=⅓πr²h), cube, rectangular prism, pyramid, and more — with unit conversion between cubic feet, liters, gallons, and cubic meters.
Disclaimer
The results provided by this tool are for informational purposes only and do not constitute medical advice, diagnosis, or treatment. Always seek the advice of your physician or other qualified health provider with any questions you may have regarding a medical condition.